Compaction of elastic granular materials: inter-particles friction effects and plastic events

Method for Determining the Coefficient of Friction Variation Pattern as a Function of Density at Low Temperatures Using the Example of Dry Ice-Steel Contact

The developments in manufacturing technologies are expected to reduce energy input without compromising product quality. Regarding the material densification process, numerical simulation methods are applied to achieve this goal. In this case, relevant material models are built using functions that describe the variation in mechanical parameters of the material in question due to its deformation. The literature review conducted for this research has revealed a shortage of experimental research methods allowing a determination of the coefficient of friction at low temperatures, approximately 200 K. This article proposes a method for determining the friction coefficient of dry ice sliding against steel. The experimental results were analysed to obtain several functions describing the variation in the coefficient of friction. These functions were then compared using goodness-of-fit indexes. Finally, two functions with similar goodness-of-fit values were chosen. The findings of this research project will complement the already available information and may be used in various research and implementation projects related to the development or improvement of currently used crystallised carbon dioxide conversion processes.

A soft departure from jamming: the compaction of deformable granular matter under high pressures

The high-pressure compaction of three dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by bonds. A simple multibody interaction is introduced to control Poisson's ratio and the arrangement of particles on the surface of a grain is varied to model both high- and low-frictional grains. At low pressures, the growth in packing fraction and coordination number follow the expected behavior near jamming and exhibit friction dependence. As the pressure increases, deviations from the low-pressure power-law scaling emerge after the packing fraction grows by approximately 0.1 and results from simulations with different friction coefficients converge. These results are compared to predictions from traditional discrete element method simulations which, depending on the definition of packing fraction and coordination number, may only differ by a factor of two. As grains deform under compaction, the average volumetric strain and asphericity, a measure of the change in the shape of grains, are found to grow as power laws and depend heavily on the Poisson's ratio of the constituent solid. Larger Poisson's ratios are associated with less volumetric strain and more asphericity and the apparent power-law exponent of the asphericity may vary. The elastic properties of the packed grains are also calculated as a function of packing fraction. In particular, we find the Poisson's ratio near jamming is 1/2 but decreases to around 1/4 before rising again as systems densify.

Experimental Compaction of a High-Silica Sand in Quasi-Static Conditions

In the compaction process, an uneven densification of the powder through the entire height of the die is a major problem which determines the strength properties of the final product, which vary throughout the entire volume. The aim of this investigation was to determine the distribution of the forming pressure inside the die and to visualise the differences in compaction. To determine the pressure inside the die during the compaction process, the deformation on the die surface was measured by means of strain gauges. However, in order to visualise the densification of high-silica sand during the compaction process, an X-ray tomograph was used, which permits one to visualise the interior of the die. The authors developed an analytical model of how the change in internal pressure influences the change in stresses arising on the outer surface of the die, and, as a result, the friction force. It has been observed that the highest values of pressure as well as the highest concentrations of the loose medium are found closest to the punch and decrease with distance from the punch. Moreover, based on the measurements of deformation, a dependence of the pressure distribution on the value of friction forces was observed, which prompted further analysis of this phenomenon. As a result, tests to determine the coefficient of friction between the die and the loose medium were carried out. This made it possible to describe the pressure distribution inside the die, based on the pressure applied and the height of the die.

Three-dimensional compaction of soft granular packings

This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to 1, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increases, a transition is observed from a granular-like material with exponential tails of the shear stress distributions to a continuous-like material characterized by Gaussian-like distributions of the shear stresses. We develop an equation that describes the evolution of the packing fraction as a function of the applied pressure. This equation, based on the micromechanical expression of the granular stress tensor, the limit of the Hertz contact law for small deformation, and the power-law relation between the packing fraction and the coordination of the particles, provides good predictions from the jamming point up to very high densities without the need for tuning any parameters.

Micromechanical description of the compaction of soft pentagon assemblies

We analyze the isotropic compaction of assemblies composed of soft pentagons interacting through classical Coulomb friction via numerical simulations. The effect of the initial particle shape is discussed by comparing packings of pentagons with packings of soft circular particles. We characterize the evolution of the packing fraction, the elastic modulus, and the microstructure (particle rearrangement, connectivity, contact force, and particle stress distributions) as a function of the applied stresses. Both systems behave similarly: the packing fraction increases and tends asymptotically to a maximum value ϕ_{max}, where the bulk modulus diverges. At the microscopic scale we show that particle rearrangements occur even beyond the jammed state, the mean coordination increases as a square root of the packing fraction, and the force and stress distributions become more homogeneous as the packing fraction increases. Soft pentagons experience larger particle rearrangements than circular particles, and such behavior decreases proportionally to the friction. Interestingly, the friction between particles also contributes to a better homogenization of the contact force network in both systems. From the expression of the granular stress tensor we develop a model that describes the compaction behavior as a function of the applied pressure, the Young modulus, and the initial shape of the particles. This model, settled on the joint evolution of the particle connectivity and the contact stress, provides outstanding predictions from the jamming point up to very high densities.

A micro-mechanical compaction model for granular mix of soft and rigid particles

We use bi-dimensional non-smooth contact dynamics simulations to analyze the isotropic compaction of mixtures composed of rigid and deformable incompressible particles. Deformable particles are modeled using the finite-element method and following a hyper-elastic neo-Hookean constitutive law. The evolution of the packing fraction, bulk modulus and particle connectivity, beyond the jamming point, are characterized as a function of the applied stresses for different proportion of rigid/soft particles and two values of friction coefficient. Based on the granular stress tensor, a micro-mechanical expression for the evolution of the packing fraction and the bulk modulus are proposed. This expression is based on the evolution of the particle connectivity together with the bulk behaviour of a single representative deformable particle. A constitutive compaction equation is then introduced, set by well-defined physical quantities, given a direct prediction of the maximum packing fraction φmax as a function of the proportion of rigid/soft particles.

Rheology of soft granular materials: uniaxial compression

Soft granular materials are assemblies of highly deformable grains interacting via surface forces. The large grain deformations of these materials differ them from hard granular systems, in which, their behaviors are essentially governed by grain rearrangements. In this paper, we study the uniaxial compression of soft granular materials using a numerical approach based on the Material Point Method allowing for large grain deformations, coupled with the Contact Dynamics method for the treatment of unilateral frictional contacts between grains. Considering the neo-Hookean and elasto-plastic grains, the compaction of 2D soft granular packings is analyzed. We focus essentially on the evolution of the packing vertical stress as a function of the packing fraction and the predictive models are proposed.

Compaction of mixtures of rigid and highly deformable particles: A micromechanical model

We analyze the isotropic compaction of mixtures composed of rigid and deformable incompressible particles by the nonsmooth contact dynamics approach. The deformable bodies are simulated using a hyperelastic neo-Hookean constitutive law by means of classical finite elements. We characterize the evolution of the packing fraction, the elastic modulus, and the connectivity as a function of the applied stresses when varying the interparticle coefficient of friction. We show first that the packing fraction increases and tends asymptotically to a maximum value ϕ_{max}, which depends on both the mixture ratio and the interparticle friction. The bulk modulus is also shown to increase with the packing fraction and to diverge as it approaches ϕ_{max}. From the micromechanical expression of the granular stress tensor, we develop a model to describe the compaction behavior as a function of the applied pressure, the Young modulus of the deformable particles, and the mixture ratio. A bulk equation is also derived from the compaction equation. This model lays on the characterization of a single deformable particle under compression together with a power-law relation between connectivity and packing fraction. This compaction model, set by well-defined physical quantities, results in outstanding predictions from the jamming point up to very high densities and allows us to give a direct prediction of ϕ_{max} as a function of both the mixture ratio and the friction coefficient.